Problem: Solve for $x$. Enter the solutions from least to greatest. $(2x +4)(3x -2)=0$ $\text{lesser }x = $
For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(2x +4)(3x -2)=0$. So either $(2x +4)=0$ or $(3x -2)=0$ : $\begin{aligned} (1)&&2x +4&=0 \\\\ &&2x&=-4 \\\\ &&x&=-2 \end{aligned}$ $\begin{aligned} (2)&&3x -2&=0 \\\\ &&3x &= 2 \\\\ &&x&=\dfrac{2}{3} \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -2 \\\\ \text{greater } x &= \dfrac{2}{3} \end{aligned}$